iOS code for saving "Open In" file to Documents directory (and resolving duplicate filenames)

First of all you need to set up your "Open In" behaviour by registering the file type UTI. From there follow the commented code.

AppDelegate.m

- (BOOL)application:(UIApplication *)application openURL:(NSURL *)url sourceApplication:(NSString *)sourceApplication annotation:(id)annotation
{

    // Copy the file into the documents directory, renaming if there's a duplicate
    [self copyItemAtURLtoDocumentsDirectory:url];

    return YES;
}



-(BOOL)copyItemAtURLtoDocumentsDirectory:(NSURL*)url {

    NSError *error;
    NSURL *copyToURL =  [self applicationDocumentsDirectory];

    NSString *fileName = [url lastPathComponent];

    // Add requested file name to path
    copyToURL = [copyToURL URLByAppendingPathComponent:fileName isDirectory:NO];   

    if ([[NSFileManager defaultManager] fileExistsAtPath:copyToURL.path]) {

        // Duplicate path
        NSURL *duplicateURL = copyToURL;
        // Remove the filename extension
        copyToURL = [copyToURL URLByDeletingPathExtension];
        // Filename no extension
        NSString *fileNameWithoutExtension = [copyToURL lastPathComponent];
        // File extension
        NSString *fileExtension = [url pathExtension];

        int i=1;
        while ([[NSFileManager defaultManager] fileExistsAtPath:duplicateURL.path]) {

            // Delete the last path component
            copyToURL = [copyToURL URLByDeletingLastPathComponent];
            // Update URL with new name
            copyToURL=[copyToURL URLByAppendingPathComponent:[NSString stringWithFormat:@"%@–%i",fileNameWithoutExtension,i]];
            // Add back the file extension
            copyToURL =[copyToURL URLByAppendingPathExtension:fileExtension];
            // Copy path to duplicate
           duplicateURL = copyToURL;
            i++;

        }


    }

    BOOL ok = [[NSFileManager defaultManager] moveItemAtURL:url toURL:copyToURL error:&error];

    // Feed back any errors
    if (error) {
        NSLog(@"%@",[error localizedDescription]);
    }

    return ok;
}

-(NSURL *)applicationDocumentsDirectory {

    NSString *documentsDirectory;
NSArray *paths = NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES);
if ([paths count] > 0) {
    documentsDirectory = [paths objectAtIndex:0];
}
// Important that we use fileURLWithPath and not URLWithString (see NSURL class reference, Apple Developer Site)
    return [NSURL fileURLWithPath:documentsDirectory];
}

Currently this places all of the code within the AppDelegate file, which of course probably wouldn't be your choice within a working app, but at least it gets you started.