To assign Leads to Partners via the Falcon Tech Community (for Salesforce.com Leads), which allows each Partner to view only their own Leads, you will have to set up private access to Leads.

Falcon Tech Community Users are linked to Salesforce.com Contacts. Therefore, the record ownership for portal users is tracked by a "relationship (lookup/master-detail)" with the Contact object.
 

In Salesforce:

1. Create a new lookup from Lead to Contact. Name the field "Partner Contact".
    
2. This allows you to have a related list in the Salesforce Contact layout that shows you all the leads that a Partner contact has registered.
    

Then in the Falcon Tech Community:

1. Log in as an Administrator.

2. Go to the Setup Homepage.

3. On the left, go to Extension > force.com Connector.

4. Click on the Leads object.

5. Press the More Actions button and select Refresh.

6. Press the Edit button.

7. Under the Entity Options sections, select the field you just created in Salesforce for Community Owner Field.

8. Click Save.
    

You must now set the Lead entity to Private in the Security Role for the Community User. Note that Falcon Tech automatically populates the new field when a Partner User creates a new Lead.