Light Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 11
Situational Awareness; Workload; Distraction; Confusion; Communication Breakdown
ATC Issue All Types; Airspace Violation All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR
Air Traffic Control Provided Assistance
Airspace Structure; Staffing; Procedure; Human Factors
I was working Sectors X/Y/Z combined up with no D-side. I had Aircraft Y; Aircraft Z; and Aircraft A to ZZZ descending via the ZZZZZ arrival.  Aircraft Y had been shipped to ZZZ Approach at the time of the incident.I was working a sequence into ZZZ1; giving a clearance off of ZZZ2; giving clearances off of ZZZ3; clearances into ZZZ4 and other overflights.  This sector configuration encompasses a lot of airspace and a small scale.I had Aircraft X check in at FL240 at the same time about 3 other aircraft call on other transmitters. One of them canceling at ZZZ1. I did not have the handoff on Aircraft X who was deviating into my ZZZ arrivals.  I immediately turned Aircraft X to a heading of 260 for traffic then to a 240 heading.  I told Aircraft Z to expedite their descent to through FL230. Aircraft A was already talking to Approach. The aircraft were about 11 miles head on when positive separation was achieved we had about 7.9 miles.Aircraft X was put on my frequency without a call or completed handoff. At that location there are also a lot of limited data blocks associated with Approach. Sector A had the handoff and told Aircraft X he was cleared to deviate left when able ZZZ5.  Sector A flashed Aircraft X to Sector B/C. Sector D/C flashed the aircraft onto me at Sector X.  Controllers are not following the rules.  They are waiting too long before calling for handoffs or pointouts.  It is too late when the aircraft is in the other person's airspace.  There is zero accountability any more.The Controller on Sector B really needs to be talked to and put on some kind of a plan.  He does not comply with the rules and procedures.  I had previously talked with the Supervisor after a very busy session on Sector B which he was on my D-side and did absolutely nothing to help.  Now he was the Controller on B/C who flashed through the Aircraft X to me and did not ensure a handoff.We need [to] return all controllers to work.  We need to have a lot of refresher training because controllers are not following procedures.
Center Controller reported an airborne conflict while working combined sectors and cited handoff related issues contributed to the event.