Ah, the Rangers. You remember them. Went on a nice run for most of the decade. Trained their eyes on the prize. Made some mistakes trying to attain it. Fell short. Fired the coach. Hired a brand-new one. Have been out of sight for weeks waiting ’til next year.

But with the Capitals’ victory in the Cup finals and the ensuing Bacchanalia behind us, the hockey calendar has turned to 2018-19, and not a moment too soon. Boy, it’s a long offseason when the games end with the first weekend of April, isn’t it? What’s striking is how commonplace this is for essentially a full third of the parity-obsessed league.

Chances are that if the Rangers make a substantial move leading into Friday’s first round of the entry draft in Dallas, it will involve Kevin Hayes. Multiple sources report the 26-year-old impending Group II free-agent center has attracted significant interest from around the league as general manager Jeff Gorton sifts through various scenarios both connected to and independent of improving the club’s ninth-overall position.

The Blueshirts have talked with Carolina about moving up to second overall, where the team would jump all over right wing Andrei Svechnikov, but though the dynamic could change through the week, such a deal seems extremely unlikely.

And while the cost of doing business could change on the draft floor, the price of moving up 3-8 spots appears prohibitive for the Blueshirts, who may be able to get their man — perhaps winger Oliver Wahlstrom, committed to BC; perhaps righty defenseman Evan Bouchard of OHL London — right where they are.

But Gorton, whose team also holds the 26th and 28th selections, is expected to make a move or two this week. In addition to Hayes, Jimmy Vesey, Ryan Spooner and Vladislav Namestnikov are also impending restricted free agents. All have been qualified, Slap Shots has learned, but the chances of them all being on the ice for David Quinn’s first training camp range from none to none.

At this point, too, the Blueshirts have a glut in the middle, with eight potential centers — Mika Zibanejad, Hayes, Filip Chytil, Lias Andersson, Namestnikov, Spooner, Boo Nieves and Brett Howden — vying for spots. No, it’s not as if Quinn will have to decide how to apportion ice time among Steve Yzerman, Sergei Fedorov and Keith Primeau as Scotty Bowman did a couple of decades ago, but still, center is one area in which the Rangers have at least a promise of depth.

Teams have been nibbling at Spooner, arbitration-eligible and one year away from unrestricted free agency, but it is Hayes, in the very same contractual spot, who has the most value on the market. Coming off a year in which he scored a career-high 25 goals while embracing his role as a matchup center, Hayes will likely command a five-year deal in the neighborhood of $4.75 million per.

The Rangers have the space, but that is second-line money for a player the team projects as its third-line center, for if Chytil makes the team out of camp — and if he doesn’t, it will be a disappointment — he will get a top-six opportunity. A depth chart of Zibanejad, Chtyil and Hayes leaves the fourth line for Andersson, and is that really what the Rangers want to do with last year’s seventh-overall pick if he is ready this time? Then there is Howden, generally projected as a third-liner. Again, a glut.

The Rangers don’t seem keen on including Hayes in a deal to move up a few spots in the first round. The inference is that if he’s moved, it would be as the centerpiece as a deal to add a righty defenseman. Winnipeg’s Jacob Trouba seems out of reach, but the Flames could be make for an interesting match. There seems to be little interest in dealing for Dougie Hamilton, but, and we have made this point before, the Blueshirts might be able to get Adam Fox, the Harvard defenseman who paired with lefty prospect Ryan Lindgren for Team USA at the past two World Junior tournaments.

Neither Vesey nor Namestnikov carry enough heft on the market to merit a substantial return on his own, but it is possible that one or the other — I would prefer that Vesey gets a shot playing for Quinn — could go as part of a package including one of the late first-round picks in draft floor maneuvering.

The Rangers have no interest in putting a skeleton squad on the ice in October. Unless there is a dramatic shift this week, Mats Zuccarello is therefore expected to report for duty at training camp heading into the final year of his contract.

Gorton is believed to have talked with Edmonton, and might be willing to accept Milan Lucic and his five-year, $30 million contract commitment if Leon Draisaitl comes the other way. There is, however, zero evidence the Oilers have the slightest inclination to make a deal like that, even if it would involve, say Brady Skjei, also an impending Group II free agent.

Brendan Smith, meanwhile, has remained in New York following the season in order to work on his fitness with Ben Prentiss. The Rangers expect him to not only be in the mix for a job, but to be the player to whom they awarded that four-year, $17.4 million deal last June.

Ilya Kovalchuk has not eliminated the Rangers from his list, but we’re told that the dynamic free agent winger would only come to Broadway if the Blueshirts acquire a player or two who would vault the club into contending status. In other words, probably not.

Quinn, who has already met with a number of players, is expected to travel to Sweden early next month in order to chat with Henrik Lundqvist, and perhaps Zibanejad and Jesper Fast. Though Lindy Ruff is going to remain part of the coaching staff in a position yet to be determined, the Blueshirts appear to be waiting on assistants whose contracts with other organizations expire on June 30 before filling their staff.

We wonder if Boston’s Joe Sacco, who was head man in Colorado while Quinn was his assistant in 2012-13, might be a target.

The Rangers do have cap space to take on another team’s problem contract but have no intention of becoming a depository for faded veterans. But if the Penguins were to often a sweetener along with Carl Hagelin, with one year at $4 million on his deal, then maybe.

And if Tampa Bay has the need to move Ryan Callahan, who has two years at $5.8 million per remaining on his deal, the Rangers could be in. That, by the way, is assuming Callahan — who probably will miss the first month or so of the season recovering from shoulder surgery — does not have the Blueshirts on his no-trade list.

This is just me, but if the Blueshirts could get Callahan (with a suitable inducement), I’d sew that “C” back on his sweater the moment the hypothetical deal were completed.