I'm asking because approach in my company looks as follows:
- stories in the backlog are not estimated
- team that picks the story estimates it in story points during sprint planning part two
Each team will have its own velocity and measurement for story points. Remember story points are not absolute, they are relative measures of complexity. If team A has a 20 point velocity and team B has a 40 point velocity, giving team A 20 points as estimated by team B might result in team A being underutilized or it might be way more than team A might be able to handle in a sprint.
Allow the teams to select which stories they will work on and estimate the points for those stories independently.
The way we approach this is on our Sprint Planning Day we have the teams all sit own and play a bit of Planning Poker with each task. Since our backlog is already well ordered by importance by our product owners and our development teams this is a simple process for us to work down that backlog and estimate until the sprint is full for each team with what they are going to work on.
Each team as a velocity so when doing the planning sessions that team knows roughly how much will fit into their sprint. All teams work together on that day to determine which team is best at getting what they are good at. No team estimates another teams work and if for some reason one team picks up a task from another team they will re-estimate it. Often in our organization the story points come out roughly the same, but not always and any issues are raised to the Scrum Master and Product Owner.
During the planning though I do make sure all the teams are working together for the estimation. This means that although Team A is going to be doing the particular story and they estimated it for X story points, someone from Team B for instance can mention have you thought about such and such as I think the estimate would be larger/smaller because of this. Our Sprints are only a couple weeks and we only have 3 sprint teams so this entire process never consumes more than a day, and usually only 4-5 hours.
The sprint planning session is part of our regular corporate heartbeat now and it works very well for us. We haven't run into a problem of one team estimating all the story points for another team to complete as stated above. I would make sure you let the teams that are doing the work estimate the work, but have everyone as engaged as necessary without it becoming burdensome.